At this point, we recall that Ref. [1]} also studied in similar terms the pole position of the \(\sigma \)  resonance by unitarizing the LO isoscalar scalar \(\pi \pi \)  PWA in the chiral limit, and the same secular equation as Eq. () was found.
It is also instructive to compare its numerical solution \(x_\sigma =0.07-i\,0.20\)  (the same one as given above for the graviball), with the value from the GKPY equations for the actual physical pion mass, \(x_\sigma =0.09-i\,0.20\) , being remarkably close to each other.
